1. Membrane Trafficking: a) Membrane wave: In collaboration with Dr. Min Wu from National University of Singapore, we established a mechanochemical feedback model that accounts for the ultrafast rhythmic propagation (>1micron/sec) of the endocytic machine on plasma membrane in immune cells. Following our previous model, we found that immune cells exhibit stimulation-dependent traveling waves within the cortex, much faster than typical cortical actin waves. These waves reflect rhythmic assembly of both actin machinery and periphery membrane proteins such as F-BAR domain-containing proteins. Combining theory and experiments, we develop a mechanochemical feedback model involving membrane shape changes and F-BAR proteins that drive oscillations and render the cortex excitable. We show that this excitability manifests itself as waves of cortical proteins that are not limited by protein diffusions along membrane. Instead, the spatial gradient in the timing of the adjacent oscillations on the cortex gives the impression of spatial propagation. The resulting phase speed dictates the observed fast propagation speeds. We provide evidences that oscillatory membrane shape changes accompany such rhythms, excite further cortical activation, and potentiate propagation beyond the initial cortical activation site. Therefore, membrane shape change has underappreciated roles in setting high-speed signal transduction rhythms across the entire cortex.This paper is under review in Current biolgy. b) We constructed a mechanical model that describes the fate of post-fusion vesicle in exocytosis a key metabolic and signaling process for a cell. It involves vesicle fusion to the plasma membrane, followed by the opening of a fusion pore, and the subsequent release of the vesicular lumen content into the extracellular space. While most modeling efforts focus on the events leading to membrane fusion, how the vesicular membrane remodels after fusing to plasma membrane remains unclear. This latter event dictates the nature and the efficiency of exocytotic vesicular secretions, and is thus critical for exocytotic function. We provide a generic membrane mechanical model to systematically study the fate of post-fusion vesicles. We show that while membrane stiffness favors full-collapse vesicle fusion into the plasma membrane, the intravesicular pressure swells the vesicle and causes the fusion pore to shrink. Dimensions of the vesicle and its associated fusion pore further modulate this mechanical antagonism. We systematically define the mechanical conditions that account for the full spectrum of the observed vesicular secretion modes. Our model therefore can serve as a unified theoretical framework that sheds light on the elaborate control mechanism of exocytosis. 2. Cell Division: a) Universal size scalings of mitotic spindle: The size of mitotic spindle scales with cell sizes in mitosis across different species and across serveral orders-of-magnitude. An universal scaling law is emerging in mitosis field as evidenced in experiments. While most of efforts have been focusing on how the mitotic spindle assembles on the mechanistic level to yield such size scaling, we took a different perspective and explored the functional role of such universal scaling relationship. We found that the allometry of mitotic spindle serves the purpose of ensuring the robustness in mitotic spindle assembly checkpoint silencing, which appears to be a universal phenomenon across animal kingdom. This paper is published in Biophysical Journal. b) SAC silencing in closed mitosis: We applied a similar SAC silencing mechanism as in open mitosis to closed mitosis, e.g. in budding yeast. We show that this spatial-temporal model can ensure the robustness of SAC silencing in closed mitosis. The poleward convection is unnecessary for the purpose of SAC silencing in closed mitosis, as conferred by the reduced dimensions of the mitotic apparatus and the closed confinement by nuclear envelope in closed mitosis. More importantly, the unique geometry of mitotic apparatus dictates that ploidy and sizes of nucleus and spindle pole body need to properly scale with each other in order for robust SAC silencing. This insight not only offers a unique and coherent explanation for diverse SAC silencing phenotypes observed in yeasts, but also suggests an evolutionary path that defines the karyotypes in present-day organisms and species. This work in under review of Biophysical Journal. c) The mechanochemistry of low-copy-number plasmid segregation machinery The segregation of DNA prior to cell division is essential for faithful genetic inheritance. In many bacteria, segregations of low-copy-number plasmids involve an active partition system composed of a ParA ATPase and its stimulator protein ParB. The ParA/ParB system drives directed and persistent movement of DNA-cargo both in vivo and in vitro. As ParA could form filaments in vitro, filament-based models akin to actin/microtubule-driven motility were proposed for plasmid segregation. Recent experiments challenge this view and suggest that ParA/ParB system motility is driven by a diffusion-ratchet type model, in which ParB-coated plasmid both creates and follows a ParA gradient on the nucleoid surface. However, the detailed mechanism of ParA/ParB-mediated directed and persistent movement remains unknown. Here we develop a theoretical model describing ParA/ParB-mediated motility. We establish that the ParA-ParB bond effectively couples the ATPase dependent cycling of ParA to motion of the ParB bound cargo. Paradoxically, this processive motion relies on quenching diffusive plasmid motion through transient ParA/ParB-mediated tethering to the nucleoid surface. Our work thus sheds light on a new emergent phenomenon in which non-motor proteins work collectively via mechanochemical coupling to propel cargos an ingenious solution shaped by evolution to cope with the lack of processive motor proteins in bacteria.This paper is under review in Biophysical Journal. 3. Cell Motility: a) Mechanochemistry of focal adhesion formation: Durotaxis cells prefer to migrate toward stiffer substrate is important for many physiological processes. Focal adhesion (FA) is a dynamically formed organelle, serving as the foot of migrating cells. We provided the first theoretical model that integrates the contributions of branched actin network and stress fiber in the FA formation. The model predicted two traction force peaks emerging within the growing FA: While the distal traction peak originates from the catch bonds that mediate FA-retrograde actin flux engagement, the central one is generated by the actomyosin contractility from stress fiber. The centraal traction peak oscillation due to the stress fiber-mediated negative feedback optimizes the range of FA mechanosensing on substrate stiffness. The competition between the two sources of tractions gives rise to the traction peak oscillation within single FAs. We experimentally verified these unique model predictions. Our study thereby establishes the coherent picture of FA formation. This paper is under 2nd round revision for Biophysical Journal. b) Fingering growth of focal adhesion: FA is heterogeneous within the same cell and across different cell types. Without a coherent model, this heterogeneity makes it difficult to analyze FA. We further extended our previous model on FA growth to explain the entire spectrum of FA growth pattern, in particular, FA could break into pieces during growth that eventually form finger-like parallel stripes. Our model establishes a unified theoretical framework that coherently accounts for FA growth under different conditions, and can serve as a guide for experiments. This paper is under review in Biophysical Journal